Talks by Session and Room (with Abstracts)

Optimal funding rates for perpetual futures: a Stackelberg game approach

Philippe Bergault (Université Paris-Dauphine (PSL)) · Sébastien Bieber (Université Paris-Dauphine (PSL)) · Olivier Guéant (Université Paris-Cité)

This paper studies the design of funding mechanisms in perpetual futures markets through a Stackelberg game between a trading platform and a representative arbitrageur. The platform chooses a funding-payment process to keep the perpetual futures price aligned with the spot price while avoiding excessive transfers that may destabilize the market or discourage participation. In response, the trader optimally builds positions in the spot and perpetual markets, accounting for trading costs, permanent price impact, and inventory risk. We characterize the trader's optimal response through a linear-quadratic stochastic control problem and derive the platform's optimal policy as the solution of a coupled forward-backward stochastic differential equation. The resulting framework provides a tractable model for studying how transfer mechanisms shape arbitrage incentives and market stability in perpetual futures markets.

Liquid Staking and the Limits of Policy

Faycal Drissi (University of Oxford) · Basil Williams (Imperial College London) · Zachary Feinstein (Stevens Institute of Technology)

We study the role of liquid staking and how it affects the interaction between issuance policy, economic productivity, and security in proof-of-stake blockchains. In a dynamic macro-finance framework, we show that issuance redistributes resources from productive on-chain activity to validators, which effectively acts as a tax on productive capital. This mechanism generates a Laffer-curve-type tradeoff: beyond an interior optimum, higher issuance weakens the productive base that finances security and reduces staking rewards. We then introduce liquid staking, which allows users to earn staking rewards while retaining liquidity for productive use. Liquid staking collapses the traditional tradeoff between staking and DeFi. When liquid staking tokens (LSTs) closely substitute for the native asset and benefit from strategic complementarities, issuance reallocates productive activity toward LSTs, compresses the feasible policy space, and can render issuance and slashing ineffective as policy instruments.

Modeling the risks within the lending-borrowing protocol Aave

Emmanuel Gobet (Sorbonne University) · Louis Latournerie (École Polytechnique)

Decentralized Finance (DeFi) lending and borrowing protocols enable investors to take leveraged long and short positions on digital assets without centralized intermediaries, but expose them to a distinctive form of risk: on-chain liquidation triggered by debt and collateral value fluctuations. In this talk, we provide a detailed formalization of Aave's lending, borrowing, and liquidation mechanisms, grounded in the protocol's open-source implementation. In doing so, we propose a mathematical modelling of the risks, including some stochastic approximations with the purpose of efficient analysis, with different applications. Among them, portfolio optimization problem.

Reputational Concerns in Delegated Staking Protocols

Julien Prat (IP Paris) · Boyang Mu (IP Paris)

Delegated staking protocols allow operators to validate blockchain networks using external funds, enhancing capital efficiency but creating a moral hazard problem in which operators bear limited financial repercussions. We show that, absent reputational concerns, delegated staking is insecure: operators exploit every attack opportunity regardless of the severity of slashing penalties. Introducing a dynamic reputation mechanism, in which the market learns about operator types from their track records, we demonstrate that reputation disciplines operators through the threat of losing future income. Our results provide a theoretical foundation for the design of securities in protocols with delegated stake.

From Economic Explanation to Performance Improvement in Machine-Learning Portfolios

Mihai Cucuringu (UCLA and University of Oxford) · Yunqi Liang (University of Oxford) · Stefan Zohren (University of Oxford)

To extend conventional model-level feature importance to economically meaningful portfolio outcomes and decisions, we propose a local first-order attribution-propagation framework that maps allocation-function feature exposures to local sensitivities of sequential portfolio performance metrics. We relate the propagated attributions to Shapley values defined directly for portfolio objectives and derive statistical inference for Sharpe-ratio attributions. The resulting attribution-guided feature-exposure intervention enables post-training adaptation, translating portfolio-metric explanations into out-of-sample decisions without retraining the underlying allocation model. We further introduce temporal stabilisation and cross-model averaging as complementary regularisation mechanisms. Empirically, the interventions yield statistically significant improvements in net Sharpe ratios across different model classes.

New: Directed Graph Clustering for Lead-Lag Structure: A Market Tug-of-War

Mihai Cucuringu (UCLA / University of Oxford)

We develop spectral methods for clustering directed networks, with a focus on uncovering lead-lag structure in high-dimensional financial time series. We leverage statistical inference under directed stochastic block models to derive a likelihood-based objective for community detection, and show how its spectral relaxation yields an efficient clustering algorithm with theoretical guarantees. A task of major interest in financial applications is estimating lead-lag relationships across assets and assessing their value for forecasting future returns. We provide a brief survey of the lead-lag detection literature, spanning core finance approaches and recent statistical and machine learning methods. By constructing directed networks from decompositions of returns into overnight and daytime components, we uncover a market-wide “tug-of-war,” whereby overnight speculation and intraday price correction propagate across stocks. Clustering these directed lead-lag networks reveals groups of leaders and laggers that yield statistically significant structures and predictive signals for cross-asset returns, which we evaluate through economically meaningful trading strategies.

Hierarchical NIG Factor Model: An EM-Based Estimation Approach

Luca Luigi Alberici (Bayes Business School) · Laura Ballotta (Bayes Business School) · Gianluca Fusai (Bayes Business School)

The aim of this paper is to estimate a non-Gaussian factor model by exploiting a hierarchical representation of the underlying distributions, which allows the model to be naturally expressed in terms of latent variables and substantially simplifies statistical inference. Within this framework, parameter estimation is carried out using the Expectation-Maximization (EM) algorithm, which efficiently leverages the mixture representation to handle latent components in an iterative and tractable manner.

In particular, we revisit the multivariate Normal-Inverse Gaussian (NIG) factor model, formulated as a Gaussian-Inverse Gaussian mixture, by allowing the latent mixing variable to affect both the mean and the variance of the Gaussian distribution. This extension enhances model flexibility and robustness while preserving analytical tractability through the hierarchical specification.

Symmetry-Aware Neural Covariance and Cross-Covariance Forecasting in Non-Stationary Financial Markets

Christian Bongiorno (CentraleSupélec) · Efstratios Manolakis (Università di Catania) · Rosario Nunzio Mantegna (Università degli Studi di Palermo)

Random-matrix theory provides asymptotically optimal shrinkage rules for large covariance and cross-covariance matrices: noisy empirical eigenvalues or singular values are regularized while the corresponding empirical modes are preserved. In real financial data, however, the assumptions underpinning these analytical formulas are often violated by non-stationarity, heavy tails, and dominant market-wide factors. This talk presents a symmetry-aware machine-learning framework that retains the theoretical structure of rotationally invariant shrinkage, while learning data-driven corrections when markets deviate from the stationary limit. I will discuss applications to end-to-end global minimum-variance portfolio construction and to cross-covariance forecasting through singular-value learning. Across both problems, embedding the analytical estimator as a limiting case yields lower out-of-sample risk and more stable dependence forecasts. Empirically, the resulting variance reduction is economically meaningful, as it supports a broader leverage region with improved drawdown control and reduced compounding erosion.

Improved approximation of Greeks in the deep parametric PDE method

Linus Wunderlich (Queen Mary University of London)

Neural-network-based solvers can compute derivative prices in high dimensions without requiring reference prices. The deep parametric PDE method extends this by approximating prices across a range of market and option parameters using a single neural network. While it enables direct evaluation of Greeks via automatic differentiation, the accuracy varies. Sensitivities with respect to underlying assets like Delta are often well-approximated, but parameter-sensitivities like Vega are not. To improve the approximation of important Greeks, we add the PDE governing the sensitivity of the price with respect to model parameters to the loss function. This approach improves the approximation of Greeks across parameters, improving the reliability of Greeks, e.g. required for sensitivity-based margin calculations such as SIMM.

Numerical valuation of American options and their Greeks under the two-asset Kou jump-diffusion model

Karel In't Hout (University of Antwerp)

This talk deals with the numerical solution of the two-dimensional time-dependent partial integro-differential complementarity problem (PIDCP) that holds for the value of American-style options under the two-asset Kou jump-diffusion model. Following the method of lines, we derive an efficient numerical method for the pertinent PIDCP. Here, for the discretization of the nonlocal double integral term, we employ an extension of Toivanen's fast algorithm (2008) in the case of the one-asset Kou jump-diffusion model. For the temporal discretization, we study a useful family of second-order diagonally implicit Runge--Kutta (DIRK) methods. Their adaptation to the semidiscrete two-dimensional Kou PIDCP is obtained by means of an effective iteration introduced by d'Halluin et al. (2004, 2005). Numerical experiments are presented that show the proposed numerical method achieves favorable second-order convergence to the American two-asset option value as well as its Greeks Delta and Gamma.

Efficient numerical valuation of American-style derivatives under two-asset infinite-activity Lévy processes

Massimiliano Moda (University of Antwerp) · Karel In't Hout (University of Antwerp) · Michèle Vanmaele (Ghent University) · Fred Espen Benth (BI - Norwegian Business School)

We propose a numerical method for approximating the values of two-asset American options under an infinite-activity exponential Lévy model for the underlying dynamics, described in [M. Moda, K.J. in 't Hout, M. Vanmaele, and F.E. Benth, (2026) arXiv:2511.02700v2].

The fair derivative value satisfies a two-dimensional partial integro-differential complementarity problem (PIDCP). The proposed numerical scheme proceeds in two steps: a finite-difference discretization in space followed by a penalty-based time-stepping method.

A major difficulty arises from the integral term in the PIDCP, which leads to a large dense matrix in the resulting semidiscrete system. The proposed method relies on a useful representation of this term, which naturally leads to a suitable discretization capable of handling the singularity. Next, a second-order implicit-explicit time-stepping scheme is employed, allowing the use of the fast Fourier transform for the semidiscretized integral term.

Numerical Methods for Impulse Control Problems in Swing Option Pricing

Mustapha Regragui (Ghent University)

We study the numerical valuation of swing options in electricity markets under a two-factor mean-reverting price model that incorporates spikes and negative prices. The contract features state-dependent waiting times determined by the exercised amount, with flexible exercise opportunities subject to local and global constraints. This framework leads to a coupled system of a parabolic partial integro-differential equation and a partial differential complementarity problem. We investigate the existence of an optimal exercise strategy and develop an effective numerical scheme to solve this coupled system.

Explicit Signal-Adaptive Sequential Optimal Execution Quotes

Fenghui Yu (TU Delft)

We present a unified explicit solution theory for optimal execution via sequential limit-order placement in a limit order book. Unlike classical execution models that control only the trading rate, our framework optimizes the quotes of individual limit orders under signal-dependent drift, price impact, inventory risk, and execution risk. We consider four widely used execution criteria, including both risk-neutral and CARA utility formulations with and without running inventory penalties. For general price-impact and inventory-penalty functions, we show that all four problems admit a common triangular finite-dimensional structure, yielding fully explicit value functions and optimal quoting strategies. We further establish well-posedness and verification results, uncover structural connections between different execution objectives, characterize long-horizon asymptotics, and demonstrate numerically how predictive signals can significantly improve optimal execution.

Enhancing Execution Strategies with Price Predictions and the Kelly Criterion

Xue Cheng (Peking University) · Yuhao Lu (Peking University) · Tai-Ho Wang (The City University of New York) · Ruixun Zhang (Peking University) · Jingbin Zhuo (Peking University)

This paper proposes a lightweight framework for improving large-trade execution by combining short-horizon price forecasts with the Kelly criterion. Unlike pre-committed benchmarks such as TWAP and VWAP, the method reallocates shares between adjacent intraday intervals according to the predicted distribution of the next price change, converting predictive signals into a controlled risk--return trade-off under logarithmic utility. To address estimation risk from finite samples, we introduce a variance-based shrinkage rule that scales the plug-in Kelly action toward zero when uncertainty is high, reducing out-of-sample aggressiveness and instability. Using Shenzhen Stock Exchange tick data for CSI 300 and CSI 500 constituents, we find consistent reductions in execution costs and modest improvements in risk-adjusted performance across several baseline schedules. The approach preserves the original schedule structure while providing a modular overlay for adaptive execution.

Controllable Generation of Implied Volatility Surfaces Using Deep Generative models

Jing Wang (Delft University of Technology) · Shuaiqiang Liu (Delft University of Technology) · Cornelis Vuik (Delft University of Technology)

Implied volatility surfaces (IVSs) are a critical input to a wide range of financial and managerial decisions, including derivative pricing, hedging, risk aggregation, and regulatory stress testing. These decisions are most consequential during periods of market stress, when IVSs exhibit extreme behavior and historical data are scarce. We present a deep generative modelling framework for controllably synthesizing IVSs that explicitly support financial and regulatory decision making. Building on variational autoencoders (VAE), we design a controllable VAE architecture, in which meaningful IVS shape characteristics are treated as interpretable control variables, while latent variables capture residual structure to preserve shape diversity. To enable this control, IVS feature values are quantified and incorporated to steer generation. The framework ensures that generated IVSs remain economically consistent and suitable for downstream pricing and risk management applications. Our results demonstrate that controllable generative AI models can serve as a practical decision-support tool for risk management.

Accelerated Share Repurchase with Power-Law Transient Impact: Tackling Non-Markovian Dynamics with Reinforcement Learning

Xue Cheng (Peking University)

This paper studies the problem of Accelerated Share Repurchase (ASR). Empirical evidence shows that market impact follows a power-law form of transient decay, which generates long-memory effects in price dynamics. This feature breaks the usual Markov structure and prevent the application of the dynamic programming principle (DPP) to the execution problem. To address this difficulty, we introduce a tractable approximation method. By bringing the ideas from Prony's method, we approximate the power-law transient impact kernel with a finite sum of exponentials and represent it by a small number of Markovian state variables. This finite-dimensional Markovian structure restores the use of dynamic programming. Building on this approximate model, we then apply reinforcement learning (RL) to learn near-optimal execution strategies under practical trading constraints. The resulting framework provides a clear balance between capturing essential market microstructure effects and maintaining computational feasibility.

This is joint work with GUO Peng and ZHUO Jingbin.

Data-Driven Stochastic Optimal Control for Trading of Renewables on Intraday Energy Markets

Chiheb Ben Hammouda (Utrecht University) · Michael Samet (RWTH Aachen University) · Raul Tempone (King Abdullah University of Science and Technology)

The growth of weather-dependent renewable generation increases price volatility and imbalance risk in power markets, motivating advanced trading strategies. We develop a continuous-time stochastic optimal control framework for intraday electricity trading based on stochastic differential equations with mean reversion to forecast trajectories. Production follows a Jacobi diffusion, while prices follow an asymmetric jump-diffusion capturing heavy tails in intraday markets. The model incorporates gate closure and energy-based imbalance settlement over the delivery window, with the path-dependent imbalance cost handled through state augmentation. The value function is characterized by two linear Kolmogorov backward equations and a nonlinear Hamilton-Jacobi-Bellman partial integro-differential equation. We solve the problem using a monotone IMEX finite-difference scheme with operator splitting and semi-implicit linearization. Numerical experiments using German market data show that the strategy outperforms the TWAP benchmark and approaches the perfect-foresight benchmark. Sensitivity analyses examine the effects of jump intensity, delivery-window length, and trading horizon on trading performance.

Optimal Strategies and Rolling Intrinsic Approaches for Battery Storage Trading in Intraday Electricity Markets: A Comparative Analysis

Karel Nana Kemajou (University of Wuppertal) · Long Teng (University of Wuppertal) · Cornelis Oosterlee (Utrecht University)

Optimizing the operation of battery energy storage systems (BESS) in intraday electricity markets requires charging and discharging decisions under uncertain and volatile electricity prices. Among the most widely used approaches are the Rolling Intrinsic (RI) strategy and Least Squares Monte Carlo (LSMC). While previous studies have compared their performance on historical market data, it remains unclear under which price dynamics one method outperforms the other and which characteristics of the price process drive these differences.

In this work, we conduct a systematic comparative analysis of RI and LSMC within a controlled synthetic market environment. Intraday electricity prices are modeled as a nonlinear transformation of a multivariate Ornstein-Uhlenbeck process, enabling systematic variation of key price dynamics. By systematically analyzing their performance across different scenarios, we identify the conditions under which each approach is most effective and provide practical guidance for selecting trading strategies in different market environments.

Italian Market Signals for Hybrid Wind--Battery Dispatch: From Price-Agnostic to Price-Driven Control

Nicolò Filippas (ERG SpA / UniGe) · Giorgia Callegaro (UniPd) · Emanuela Sasso (UniGe) · Sadion Xhuveli (ERG SpA)

The aim of this work is to show the implementation and extension of the algorithm for optimal intraday dispatch of hybrid wind-battery assets, originally developed by Aung and Ludkovski (2025), adapted to the Italian electricity market. The algorithm combines dynamic programming with Gaussian-process emulation of the value and control maps, making the Dynamic Programming Principle more practical by replacing its otherwise costly computations with efficient approximations. Its aim is to determine the optimal battery schedule that minimizes firming deviations between realized and target generation.

We calibrate the model using Italian wind production and imbalance price data, replacing the price-agnostic U.S. framework with a formulation driven by Italian market signals from the Mercato del Giorno Prima and real-time Prezzo di Sbilanciamento. The resulting control incorporates asymmetric penalties reflecting upward and downward imbalance costs specific to the Italian dispatch system.

Semi-Static hedging of volumetric risk in energy markets

Konstantinos Chatziandreou (University of Amsterdam) · Sven Karbach (University of Amsterdam)

Power purchase agreements (PPAs) support the green energy transition by fixing prices for uncertain renewable generation, typically over 10--15 years. Their value depends on the joint distribution of future renewable output and forward electricity prices. This talk presents quantitative methods for pricing PPAs and hedging their embedded risks.

We develop a coupled model for electricity forward prices and renewable production indices. A Wishart-type stochastic covariance specification captures the complex dependence between future production volumes and forward price dynamics.

We also propose a semi-static variance-optimal hedging strategy. Its dynamic component trades liquid electricity forwards, while its static buy-and-hold component holds a basket of contingent claims. Quanto indices and weather derivatives are central instruments, because they capture stochastic price--production covariance and can be structured to hedge both volume and price risk. Finally, we assess how this integrated framework mitigates the risks intrinsic to PPAs.

A Generalised Stochastic Hybrid Systems Approach to American Option Pricing

Amira Meddah (Johannes Kepler University) · Evelyn Bukwar (Johannes Kepler University) · Agnes Mallinger (Johannes Kepler University) · Sascha Desmettre (Johannes Kepler University)

This talk presents a stochastic hybrid framework for pricing American options using Piecewise Diffusion Markov Processes (PDifMPs). Unlike classical models with constant drift and volatility, PDifMPs combine continuous stochastic dynamics with discrete jumps, allowing for a more realistic representation of sudden market fluctuations and changing market regimes. The proposed approach is compared with the classical Longstaff--Schwartz algorithm, including a modified version based on PDifMP-generated asset trajectories.

Universal Approximation on Non-geometric Rough Paths and Applications to Financial Derivatives Pricing

Fride Straum (Norwegian University of Science and Technology) · Fred Espen Benth (BI - Norwegian Business School) · Fabian Andsem Harang (BI - Norwegian Business School)

We present a novel perspective on the universal approximation theorem for rough path functionals, introducing a polynomial-based approximation class. We extend universal approximation to non-geometric rough paths within the tensor algebra. This development addresses critical needs in finance, where no-arbitrage conditions necessitate Itô integration. Furthermore, our findings motivate a hypothesis for payoff functionals in financial markets, allowing straightforward analysis of signature payoffs proposed in Arribas (Derivatives Pricing Using Signature Payoffs; 2018).

Signature Kernel Ridge Regression

Jakob Kellermann (Weierstrass Institute) · Christian Bayer (Weierstrass Institute)

The signature of a path is a classical object in rough path theory that provides a complete summary of a path's behavior and has found widespread use as a feature map for sequential data. In this talk, we present recent work on kernel ridge regression with the signature kernel on spaces of stopped rough paths. We identify the associated reproducing kernel Hilbert space (RKHS) as a space of linear functionals of the signature, implying universality of the RKHS. Extending the approach of Caponnetto and De Vito to unbounded kernels satisfying moment growth conditions, we provide finite sample guarantees for signature kernel ridge regression, both for the case where the kernel fulfills a Bernstein condition, as well as for the heavy-tailed setup. Numerical experiments on rough differential equations confirm that the method performs effectively in practice.

A Chen-Strichartz representation for Lévy models with applications to stochastic covariance models

Anke Wiese (Heriot-Watt University) · Kurusch Ebrahimi-Fard (Norwegian University of Science and Technology) · Frédéric Patras (Université Côte d'Azur)

For deterministic differential equations and for continuous stochastic differential equations, the Chen-Strichartz series expansion, an expansion of the solution in terms of commutators of vector fields and iterated integrals, is well-known to play a central role in the development of numerical integration schemes that preserve qualitative properties of the solution.

For stochastic differential equations that are driven by Lévy processes, the flow map, which describes the evolution of the solution, involves additional operators arising from jumps. We will derive a Chen-Strichartz series representation, depending only on commutators of vector fields and iterated integrals, and we will provide an explicit expression for the components in this series, generalising previous results for deterministic and continuous stochastic differential equations. We will illustrate the new Chen-Strichartz series representation in the application to a multi-dimensional stochastic covariance model.

An ecological approach to credit flows in interfirm networks

Anahí Rodríguez-Martínez (University College London) · Silvia Bartolucci (University College London) · Francesco Caravelli (Los Alamos National Laboratory) · Victoria Landaberry (Banco Central del Uruguay) · Pierpaolo Vivo (King's College London) · Fabio Caccioli (University College London)

We introduce DebtStreamness (DS), a metric inspired by trophic levels in ecological food webs, to measure firms' positions within credit chains. DS captures how far credit travels through interfirm lending before reaching its final users. Applying the framework to Uruguay's interfirm credit network using Central Bank credit registry and survey data, we find a tiered, hierarchical network structure that reflects firms' positions relative to financial institutions. We show that local network motifs, particularly loops, can substantially increase a firm's DS. Using a stylized stress-test exercise, we find that firms with higher DS experience greater liquidity losses under a liquidity shortage, highlighting the value of DS for assessing risk.

Stochastic Control of Core–Periphery Banking Systems

Ben Hambly (University of Oxford) · Rawan Madi (University of Oxford) 

We study a stochastic control problem for an interbank system with a heterogeneous core-periphery structure. The model consists of a finite collection of core banks interacting with a mean-field population of periphery banks, with interactions designed to capture the different roles played by institutions within the network. The objective of the controller is to mitigate systemic risk by balancing the cost of intervention against the losses associated with bank distress and default. We introduce the model and its interaction mechanisms, present the associated PDE characterization of the control problem, and discuss numerical results illustrating the behavior of the optimal intervention strategy under different forms of interaction between the core and periphery populations.

Computing the Impact of Regulation on Systemic Risk

Nikolai Nowaczyk (The London School of Economics and Political Science)

Since the great financial crisis in 07/08, major regulation like mandatory initial margin and central clearing has been issued to mitigate counterparty credit risk in the global derivatives trading system. We study the isolated impact of such regulation by a priori estimates in a graph model of trade and risk relations of financial systems created by generative methods. We identify key drivers of impact consistent with empirical findings and provide policy makers and practitioners with tools to study the impact of regulatory interventions before implementation.

Modelling contagious bank runs

Luitgard Veraart (The London School of Economics and Political Science)

We develop a modelling framework for contagion in financial networks arising from bank runs. We show how interacting channels of contagion, namely funding withdrawals in the interbank network and price-mediated contagion arising from fire sales can turn a bank run on one institution into a systemic crisis. Furthermore, we also model how contagion effects can lead to additional bank runs. Our model allows for a wide range of withdrawal mechanisms both by banks and by external depositors. It can be used for financial stress testing and particularly for analysing implications of different withdrawal mechanisms for systemic risk. We illustrate this in stylised examples and an empirical case study. We find that the extent of systemic risk is highly sensitive to the choices of withdrawal strategies used by the market participants. We also discuss policy implications.

Signature approach for pricing and hedging path-dependent options with frictions

Eduardo Abi Jaber (École Polytechnique) · Donatien Hainaut (Catholic University of Louvain) · Edouard Motte (Catholic University of Louvain)

We introduce a novel signature approach for pricing and hedging path-dependent options with instantaneous and permanent market impact under a mean-quadratic variation criterion. Leveraging the expressive power of signatures, we recast an inherently nonlinear and non-Markovian stochastic control problem into a tractable form, yielding hedging strategies in (possibly infinite) linear feedback form in the time-augmented signature of the control variables, with coefficients characterized by non-standard infinite-dimensional Riccati equations on the extended tensor algebra. Numerical experiments demonstrate the effectiveness of these signature-based strategies for pricing and hedging general path-dependent payoffs in the presence of frictions. In particular, market impact naturally smooths optimal trading strategies, making low-truncated signature approximations highly accurate and robust in frictional markets, contrary to the frictionless case.

Reconciling P- and Q-Calibration: The Discrete-Time 4-Factor Path-Dependent Volatility Model

Julien Guyon (ENPC, Institut Polytechnique de Paris; New York University) · Léo Parent (ENPC, Institut Polytechnique de Paris)

Model calibration under P and under Q are often regarded as two separate branches of finance. One may question whether such a strict separation is justified or whether it reflects the lack of models able to capture the joint dynamics of prices and implied volatilities. Path-dependent volatility models are uniquely positioned to reconcile P- and Q-calibration, since they precisely relate past asset returns to volatility, thus to option prices. In this talk, we introduce the discrete-time 4-(or 3-)factor path-dependent volatility model and show that combining the path-dependency of volatility that we uncovered in Volatility Is (Mostly) Path-Dependent (Guyon and Lekeufack, 2023) with fat-tailed random innovations allows us to reconcile model calibration under P and under Q, which further supports the hypothesis of high endogeneity of volatility. We also propose a new estimation approach that combines P- and Q-information to enhance calibration robustness, and we benchmark its effectiveness against classical methods.

Generalizable and Interpretable Dynamic Hedging Strategies Using Itô Signatures as Tradable Bases

Xin Guo (University of California, Berkeley) · Binnan Wang (Peking University) · Ruixun Zhang (Peking University)

Joint work with Xin Guo (UC Berkeley) and Ruixun Zhang (Peking University). This paper develops an interpretable machine-learning framework for dynamic hedging using the Itô signature of asset-price paths. We show that each discretized Itô signature component can be replicated by a self-financing strategy using only the underlying assets and cash, turning Itô signatures into tradable and transparent hedging bases. This allows nonlinear derivative payoffs to be approximated by linear combinations of signature terms and hedged accordingly. We establish approximation results for Itô signatures and derive theoretical bounds for in-sample and out-of-sample hedging errors. Our method is computationally efficient, easy to implement, and avoids estimating conditional expectations. In simulations, it delivers strong sample efficiency relative to neural-network benchmarks, and in an empirical study of S&P 500 index options, it shows robust performance across contracts. Overall, the paper identifies Itô signatures as a practical, transparent, and model-free foundation for dynamic hedging.

Machine-learning regression methods for American-style path-dependent contracts

Matteo Gambara (Inait SA) · Giulia Livieri (The London School of Economics and Political Science) · Andrea Pallavicini (Intesa Sanpaolo)

Evaluating financial products with early-termination clauses, particularly those with path-dependent structures, is challenging. This contribution focuses on Asian options, look-back options, and callable certificates. We will compare regression methods for pricing and computing sensitivities, highlighting modern machine learning techniques against traditional polynomial basis functions. Specifically, we will analyze randomized recurrent and feed-forward neural networks, along with a novel approach using signatures of the underlying price process. For option sensitivities like Delta and Gamma, we will incorporate Chebyshev interpolation. Our findings show that machine learning algorithms often match the accuracy and efficiency of traditional methods for Asian and look-back options, while randomized neural networks are best for callable certificates. Furthermore, we apply Chebyshev interpolation for Delta and Gamma calculations for the first time in Asian options and callable certificates.

Is Rebalancing Bad for Your Wealth?

Peter Forsyth (University of Waterloo)

The conventional wisdom suggests that retail investors should rebalance their portfolios back to a constant weight stock-bond mix. Although this sounds reasonable, both a theoretical model and empirical tests based on block bootstrap resampling of historical data do not support this claim. At best, the evidence for rebalancing the stock-bond split (as compared with buy and hold) for time horizons of less than ten years, is weak.

Only in the case where the investor wishes to avoid high instantaneous volatility (even though the CDF of the terminal wealth is arguably superior for buy and hold) will rebalancing be the better choice.

Champagne leverage on a beer budget: rethinking leveraged ETFs for the retail investor.

Pieter Van Staden (University of Waterloo) · Peter Forsyth (University of Waterloo) · Yuying Li (University of Waterloo)

Leveraged Exchange Traded Funds (LETFs), extremely controversial in literature, remain popular with retail investors. Could their potential be underestimated? We investigate the inclusion of a broad-market LETF in long-term, dynamically-optimal portfolios for the retail investor, with an objective function designed to maximize the information ratio (IR) relative to standard benchmarks. Exploiting the observation that LETF positions deliver call-like payoffs, we show that a LETF can provide inexpensive leverage while preserving downside protection. Under stylized assumptions, we derive closed-form IR-optimal strategies using either a LETF or a standard/vanilla ETF (VETF). In more realistic settings, we adopt a neural network-based approach trained on bootstrapped historical data. IR-optimal strategies containing a LETF are more likely to outperform the benchmark than their VETF counterparts, and achieve partial stochastic dominance over both benchmark and VETF-based strategies, helping to explain the empirical appeal of LETFs to retail investors.

Variable Annuities: A closer look at ratchet guarantees, hybrid contract designs, and taxation

Jennifer Alonso-Garcia (Université Libre de Bruxelles) · Len Patrick Dominic M. Garces (UNSW Sydney) · Jonathan Ziveyi (UNSW Sydney)

This paper investigates optimal withdrawal strategies in a variable annuity contract (VA) with a guaranteed minimum withdrawal benefit (GMWB) rider incorporating taxation and a ratchet mechanism for updating the benefit base. Optimal policyholder behaviour is characterised by solving a backward dynamic programming problem maximising the discounted risk-neutral expectation of contract cash flows. Reflecting traded VA contracts, our hybrid product includes a cash fund serving as an intermediate repository of VA earnings, accruing interest at a contractually specified rate. Our results reveal significant interactions among taxation, cash fund, and benefit base update mechanism. The ratchet scheme, in contrast to the return-of-premium specification, discourages early surrender by providing stronger downside market risk protection. High tax rates amplify the tax-shielding role of the cash fund, enhancing overall contract attractiveness. However, the cash fund suppresses active withdrawals, with policyholders preferring passive transfers of the guaranteed amount, diminishing its role as a retirement solution.

Optimal for Whom? Is the Retail Investor at the Table or on the Menu?

Graham Westmacott (Richardson Wealth)

A lifecycle model is developed to investigate the relative importance of competing drivers of long-term retirement outcomes. The model incorporates historical return data, realistic household cash flows, Canadian taxation, registered and taxable accounts, public pensions, housing, retirement withdrawal policies, and consumption-based measures of retirement welfare.

Preliminary results suggest that several factors under direct household control---including spending flexibility, retirement timing, savings behaviour, and investment costs---may have effects on retirement outcomes that are comparable to, and in some cases larger than, those produced by changes in asset allocation. The objective of the presentation is to offer a computational framework that incorporates lessons from optimal stochastic control studies into a personal financial planning framework to evaluate a question of growing importance to retail investors: when planning for retirement, which decisions genuinely deserve the most attention?

Fourier-cosine Pricing for Products against Cyber Attacks

Junyou Li (Chinese University of Hong Kong) · Matteo Malavasi (UNSW Sydney) · Zhengyao Ross Sun (Celestial Scale) · Tak Kwong Wong (Shenzhen University) · Phillip Yam (Chinese University of Hong Kong)

A major challenge in emerging risk modelling in FinTech/InsurTech/RegTech is handling those real datasets where most covariates are categorical, to predict claim numbers and severities in cyber risk; this is the shortfall of commonly adopted temporal models, such as Hawkes process or autoregressive models. To address this, we propose a novel superposed marked Hawkes process integrating categorical covariate information to infer hidden clustering structures; indeed, by employing classifiers such as CIBer/CART/MLP, we iteratively optimize both model parameters and cluster partitions using mini-batch SGD. The effectiveness of this modelling is demonstrated through empirical studies with benchmark cyber risk datasets, yielding notably improven prediction for frequencies (also for severities). With the new process, all existing pricing methods should be revisited; while we here highlight the use of Fourier-COS method to effectively price different insurance products against cyber risk, particularly as a finite series involving the Laplace functional of the corresponding compound process.

Pricing vanilla options on RECs for jump-diffusion models in the generation rate.

Pablo Pérez Picos (University of A Coruña) · Carlos Vazquez Cendon (University of A Coruña) · María del Carmen Calvo Garrido (University of A Coruña)

Although international organizations and governments recognize the benefits of renewable energy, deploying the associated technologies requires substantial investments. Consequently, additional market mechanisms have been developed to support their expansion. Renewable Energy Certificates (RECs) are currently traded together with their derivatives in energy markets.

In this work, we extend previous PDE-based models for pricing vanilla options on RECs by considering a jump-diffusion process for the renewable generation rate. More precisely, in the case without jumps, a linear PDE model has been obtained when the generation rate and number of RECs are considered as underlying factors. The inclusion of jumps leads to a linear PIDE model with an additional nonlocal (integral) term with respect to the PDE model. In the present work, we also propose suitable numerical methods for the treatment of this PIDE model. Numerical examples for European and American options illustrate the behaviour of the model and the numerical methods.

Rough volatility dynamics in commodity markets

Roberto Daluiso (Intesa Sanpaolo) · Héctor Folgar-Cameán (University of A Coruña) · Andrea Pallavicini (Intesa Sanpaolo) · Carlos Vázquez Cendón (University of A Coruña)

We present a general rough volatility model for commodities that provides an automatic calibration of the initial term structure of the futures prices and an appropriate treatment of the Samuelson effect, and further allows us to promote models usually employed in equity markets into the commodity framework. After the theoretical analysis of this general model, we focus on the rHeston and rBergomi models as characterisations of the general model and calibrate them to market data of vanilla futures options on WTI Crude Oil. Finally, numerical results illustrate the performance of the proposed rough volatility models for commodities pricing.

The Space Mapping Approach in Computational Finance

Anna Clevenhaus (University of Wuppertal) · Claudia Totzeck (University of Wuppertal) · Matthias Ehrhardt (University of Wuppertal)

We present a novel approach to calibrating the parameters of the Heston model for pricing an Asian put option: space mapping. Since few Heston model parameters can be directly extracted from real market data, calibrating to real market data is implicit and challenging. Additionally, some parameters in the model are nonlinear, making it difficult to find the global minimum of the optimization problem during calibration. Our approach is based on space mapping, which exploits the residuum of a coarse surrogate model that allows optimization and a fine model that requires calibration. In our case, pricing an Asian option using the Heston model SDE is the fine model, and the surrogate is the Heston model PDE for pricing a European option. We formally derive a gradient descent algorithm for the PDE-constrained calibration model and demonstrate that the space mapping approach is useful for financial calibration tasks by showcasing some numerical results.

Modeling and Replication of the Prepayment Option of Mortgages Including Behavioral Uncertainty

Lech Grzelak (Utrecht University) · Cornelis Oosterlee (Utrecht University) · Leonardo Perotti (Utrecht University)

Prepayment risk embedded in fixed-rate mortgages forms a significant fraction of a financial institution’s exposure, and it receives particular attention because of the magnitude of the underlying market. The embedded prepayment option bears the same interest rate risk as an exotic interest rate swap with a suitable stochastic notional. We investigate the effect of relaxing the assumption of a deterministic relationship between the market interest rate incentive and the prepayment rate. A non-hedgeable risk factor is modeled to capture the uncertainty in mortgage owners’ behavior, leading to an incomplete market. We prove under natural assumptions that including behavioral uncertainty reduces the exposure’s value. We statically replicate the embedded prepayment option exposure with swaps and swaptions. We show that a replication based solely on swaps cannot easily control the right tail of the exposure distribution, while including swaptions enables that. 

Deep Joint Learning Valuation of Bermudan Swaptions

Francisco Gomez-Casanova (BBVA) · Alvaro Leitao (University of A Coruña) · Fernando de Lope (BBVA) · Carlos Vázquez Cendón (University of A Coruña)

This work addresses the problem of pricing involved financial derivatives by means of advanced deep learning techniques. More precisely, we methodically integrate several sophisticated neural network-based concepts like differential machine learning, Monte Carlo simulation-like training samples and joint learning to come up with an efficient numerical solution. The application of the latter development represents a novelty in the context of computational finance. We also propose a novel design of interdependent neural networks to price early-exercise products, in this case, Bermudan swaptions. The improvements in efficiency and accuracy provided by the approach proposed here is widely illustrated throughout a range of numerical experiments. Moreover, this novel methodology can be extended to the pricing of other financial derivatives.

Fast Finite Difference Techniques for American Options Under Negative Rates

Fabien Le Floc'h (Independent Researcher)

The classic Brennan-Schwartz algorithm to solve the linear complementary problem, which arises from the finite difference discretization of the partial differential equation related to American option pricing does not lead to the exact solution under negative interest rates. This is due to the two exercise boundaries which may appear under negative interest rate, while the algorithm was proven to lead to the exact solution in the case of a single exercise boundary only. We show that two sweeps of the Brennan-Schwartz algorithm in two directions is enough to recover the exact solution.

Hans Buehler (University of Oxford) · Blanka Horvath (University of Oxford) · Raeid Saqur (University of Oxford) · Yannick Limmer (University of Oxford) · Anastasis Kratsios (University of Toronto)

We present a smooth arbitrage-free non-parametric option surface model (SANOS), the first of this kind. We discuss fitting the market and then show how this model can be used to generate time series of arbitrage-free option surfaces both under the statistical and a risk-neural measure. (DYSANOS).

Meshless cluster induction and Gaussian Kissing

Peter Jaeckel (OTC Analytics)

We give a survey on meshless induction methods based on radial basis functions for diffusion PDEs, and their ramifications as the problem dimension is increased beyond 7. We demonstrate that the representation quality depends strongly on the cluster distribution uniformity which in turn is linked like a cliff-edge to the (Gaussian) Kissing Number.

Information Leakage and Opportunistic Trading Around the FX Fix

Johannes Muhle-Karbe (Imperial College London) · Roel Oomen (Deutsche Bank) · Mateo Rodriguez Polo (ETH Zürich)

When dealers hedge large currency fix exposures on behalf of their clients, this can lead to predictable price patterns that opportunistic traders can exploit. We show that the cost of this information leakage is predominantly borne by the client, but that it can be partially mitigated when the dealer hedges some of their exposure ahead of the fixing window. The dealer also benefits from such a strategy because it lets them average in at a hedging price that is favourable compared to where the fix is expected to settle. Information leakage therefore mitigates a conflict of interest that would otherwise exist by aligning the interests of the dealer and the client against those of the opportunistic trader.

Passive Impact

Yadh Hafsi (DeepFin Research) · Nathan Pinel (DeepFin Research) · Qi Liu (DeepFin Research)

We develop a market-impact framework for passive trading in listed futures, using tick-level MBO data to study child orders and fills far smaller than those in classical impact studies. We find material instantaneous impact: volatility-adjusted impact scales with order-flow participation and is estimated using heteroskedasticity-robust inference. Transient impact is modeled with normalized response functions, fitted using power-law and constrained multi-exponential kernels, and compared with a ridge-regularized bare propagator recovered from trade-sign autocorrelation moments. Under suitable sampling and event-grouping, the transient component consistently exhibits the power-law decay predicted by long-memory microstructure theory. The full framework is implemented with rolling out-of-sample refits.

Robust Learning Under Ambiguity in Data-Driven Trading

Ben Wood (JPMorgan Chase)

The successful application of machine learning techniques in trading, as in other areas, relies on appropriate training datasets. Implicitly, these datasets embed our beliefs about the probabilities of future events, but these beliefs are generally subject to some uncertainty, known as ambiguity.

In this talk I will introduce ambiguity and the application of ambiguity-averse decision frameworks to machine learning in trading. I will discuss the limitations of a purely worst-case approach, and present recent work on more balanced ambiguity aversion for hedging problems, which aim to deliver robustness without excessive conservatism.

There is an important distinction between static and dynamic ambiguity. In financial markets, uncertainty persists through time, even as more data arrives. I will discuss our work on the implications of non-vanishing ambiguity for dynamic trading problems, and the limitations of static ambiguity.

Continuous Time Reinforcement Learning with Regime Shifts via a Change Point Approach

Alvaro Cartea (University of Oxford) · Leandro Sánchez-Betancourt (University of Oxford) · Jonathan Tam (University of Oxford) · Horace Yiu (University of Oxford)

We develop an exact, finite-dimensional exploratory reinforcement-learning framework for continuous-time changepoint detection and control under partial observability, extending Wang et al. to a regime-switching setting with doubly unknown drift. Coupling a Wonham filter with conditional Kalman–Bucy filters over compactly supported (pre-change) and N-point discrete (post-change) priors yields a Markovian sufficient statistic driven by a single innovation Brownian motion. We construct a strict viscosity subsolution barrier and prove a comparison principle, giving well-posedness of the entropy-regularised HJB equation. Future work allows us to solve the pointwise entropy-regularised optimisation inside the HJB to yield an explicit, implementable exploration policy for linear-quadratic costs.

How much should we care about what others know? Jump signals in optimal investment under relative performance concerns

Peter Bank (Technical University Berlin) · Gemma Sedrakjan (Technical University Berlin)

We present a multi-agent and mean-field formulation of a game between investors who receive private signals informing their decisions and who interact through relative performance concerns. A key tool is a Poisson random measure driving jumps in market prices and signal processes, capturing common and idiosyncratic noise. Upon receiving a jump signal, investors evaluate not only its implications for stock price movements but also for their peers' signals and subsequent decisions. A crucial aspect is the economy's distribution of investor types, determining risk aversion, performance concerns, and signal quality and quantity. We demonstrate how these factors are reflected in HJB equations, characterizing optimal responses to peers' signal-based strategies. Equilibria existence in both games is established using Schauder's Fixed Point Theorem under suitable conditions on investor characteristics, particularly signal processes. Finally, numerical case studies illustrate these equilibria, addressing how much investors should care about the information known by their peers.

Optimal stopping and divestment timing under scenario ambiguity and learning

Andrea Mazzon (University of Verona) · Peter Tankov (ENSAE-CREST, Institut Polytechnique de Paris)

Aiming to analyze the impact of environmental transition on the value of assets and on asset stranding, we study optimal stopping and divestment timing decisions for an economic agent whose future revenues depend on the realization of a scenario from a given set of possible futures. Since the future scenario is unknown and the probabilities of individual prospective scenarios are ambiguous, we adopt the smooth model of decision making under ambiguity aversion of Klibanoff et al (2005), framing the optimal divestment decision as an optimal stopping problem with learning under ambiguity aversion. We then prove a minimax result reducing this problem to a series of standard optimal stopping problems with learning. The theory is illustrated with two examples: the problem of optimally selling a stock with ambiguous drift, and the problem of optimal divestment from a coal-fired power plant under transition scenario ambiguity.

Trading with uncertainty about signals and price impact

Johannes Muhle-Karbe (Imperial College London) · Sturmius Tuschmann (Imperial College London)

*Held in Room A

We study optimal trading with uncertainty about both trading signals and price impact. Rather than treating all models within a prespecified class as equally plausible, we penalise less likely ones according to their distance from a reference model. In the limit of small uncertainty aversion, this yields closed-form expressions for the optimal robust trading strategy. In a simulation study with noisy parameter estimates, we find that optimal regularisation via uncertainty aversion markedly improves performance compared to plug-in strategies based on point estimates only. For weak signals, impact uncertainty only plays a secondary role but rapidly becomes dominant as signal strength increases.

Efficient decumulation strategy with long-term care insurance and guaranteed minimum death benefit

Jonathan Ziveyi (UNSW Sydney) · Jennifer Alonso-Garcia (Université Libre de Bruxelles) · Mengdie Hu (UNSW Sydney) · Yuxin Zhou (UNSW Sydney)

The global shift from defined benefit to defined contribution pension systems has transferred longevity, health, and market risks to individuals, encouraging precautionary saving and restrained retirement consumption. We propose a decumulation strategy that combines long-term care insurance (LTCI) and a guaranteed minimum death benefit (GMDB), purchased at retirement, with a withdrawal-then-rebalance investment approach. Retirement wealth follows a regime-switching process, while a target-volatility strategy dynamically adjusts asset allocation to smooth wealth trajectories and limit extreme losses. LTCI insures late-life healthcare expenditures, and the GMDB secures a minimum bequest, jointly supporting consumption confidence and legacy objectives. Numerical experiments compare consumption outcomes under the proposed strategy with standard account-based pension drawdown rules. The results show smoother lifetime consumption and greater resilience to adverse market shocks. Sensitivity analyses across insurance allocations, health-state transitions, and volatility targets indicate that moderate volatility targets balance risk and sustainability and that performance is robust across health scenarios.

Execution-Aware Pairs Trading: A Stochastic Control Formulation for Illiquid Commodity Markets

Tobias Jung (Uniper Global Commodities SE)

European energy markets exhibit structurally cointegrated relationships across gas and power instruments: time spreads along the forward curve, location spreads between hubs such as TTF (continental Europe) and NBP (UK), and cross-commodity spreads driven by fuel conversion. Unlike equity markets, however, these contracts trade in illiquid order books with wide, leg-specific bid--ask spreads, small lot sizes, and infrequent executions, rendering the frictionless rebalancing assumptions underlying classical pairs-trading models untenable.

We develop an execution-aware stochastic control framework for asymmetric pairs-trading that integrates cointegrated price dynamics with realistic order-level execution frictions. Trading decisions are per-leg limit- and market-order postings under stochastic fills, inventory constraints, and imbalance penalties, yielding a coupled diffusion--jump control problem. The model is solved via a finite-horizon dynamic-programming scheme using exact one-step diffusion transitions and high-accuracy quadrature. The resulting policies illustrate how optimal pairs-trading behavior changes when execution risk and market illiquidity are incorporated directly into the control problem.

Data-Driven Duration Management: Term Structure Forecasting Using Machine Learning

Tobias Lausser (Technical University of Munich)

Predicting movements of the term structure of zero rates is a central task in fixed-income portfolio management: Small perturbations of any of the key yield-curve factors (level, slope and curvature) may have significant impact on portfolio valuation, risk metrics and relative performance. Duration management provides an intuitive investment approach: investors anticipating declining yields may increase duration to benefit from increasing prices and investors anticipating rising yields may decrease duration to limit losses. The performance of such strategies highly depends on the robustness and accuracy of the underlying yield forecasts.

In our contribution, we propose several forecasting procedures that combine classical methods and machine learning, and develop an evaluation framework based on statistical metrics and economic performance in duration management. The forecasting methods connect dimension reduction techniques and time-series forecasting in the latent space, allowing the inclusion of macroeconomic factors. We apply the framework to both U.S. and European yield-curve data.

A Causal Machine Learning Framework for Municipal Bond Spread Determinants: Japanese Evidence Around NIRP

Yasuhiro Tamba (Seinan Gakuin University) · Kentaro Haraguchi (Seinan Gakuin University) · Keiichi Oishi (Kyushu University)

We identify causal determinants of credit spreads in the Japanese municipal bond market around the January 2016 Negative Interest Rate Policy (NIRP). Using JSPrice secondary-market transactions over 2015--2020, we apply Causal Forest and Double Machine Learning, with robustness checks via 2SLS, propensity score matching, and additional methods. The real debt service ratio exhibits the largest positive causal effect on spreads across all methods. We document a structural shift around NIRP: aggregate CATE compressed by 69%, and the share of fiscal-soundness indicators in spread pricing collapsed, indicating that municipal fiscal health largely ceased to be priced under ultra-low rates, reflecting suppressed cross-municipality differentiation rather than improved market efficiency. Heterogeneity analysis shows small municipalities are about three times more fiscal-sensitive than large ones, consistent with a too-big-to-fail mechanism. SHAP-based predictive importance largely overlaps with causal rankings, while divergences reveal confounding.

Graph-based high-dimensional time series modelling for energy markets: Inference for Levy-driven graph supOU processes

Almut Veraart (Imperial College London)

In this talk, we introduce Levy-driven graph supOU processes, a parsimonious and interpretable class of models in which the dependence between components is governed by an underlying graph structure. This construction bridges short- and long-range dependence within a single parametric family while accommodating a broad class of marginal distributions, making it particularly well suited to applications in energy systems. We develop a generalised method of moments estimator for this model class, establish its consistency and asymptotic normality, and assess its finite-sample performance through a simulation study. To illustrate the practical relevance of the framework, we present an empirical application to wind capacity factors within a European electricity network, demonstrating how the graph structure can reflect the spatial and physical connectivity of energy systems.

A Principal-Agent Game of Offset Credit Markets with Strategic Risk-Averse Agents

Sebastian Jaimungal (University of Toronto) · Liam Welsh (University of Toronto)

We study a principal-agent model of a greenhouse gas offset credit market in which a regulator chooses the penalty for non-compliance and the probability that submitted projects are approved for credits, while strategic agents interact in a game when deciding whether and when to generate and trade offset credits. Agents account for price impact from generation, uncertainty in project approval, and terminal penalties, and evaluate outcomes under exponential utility to incorporate risk aversion. The principal’s (regulator's) objective is to maximize the probability that aggregate generated offset credit exceeds a prescribed minimum threshold, thereby ensuring sufficient environmental impact while maintaining market efficiency. The resulting framework combines stochastic control, game theory, and mechanism design, yielding equilibrium characterizations that highlight how penalties, approval uncertainty, and market impact jointly influence agents’ behavior and the likelihood of achieving target levels of offset generation.

Shaping volatility surfaces with optimal transport: arbitrage repair, stress-testing, and scenario generation

Marius Chevallier (Ecole Polytechnique) · Stefano De Marco (Ecole Polytechnique) · Pierre-Emmanuel Lévy-dit-Vehel (Société Générale)

We propose a framework based on optimal transport for performing risk management tasks on implied volatility surfaces. It addresses arbitrage removal, arbitrage-free stress testing, and generation of volatility surfaces. Starting from a set of implied volatilities on a discrete grid, we construct a vector of marginals consistent with the observed data. It is then transformed by minimizing a functional involving Monge-Kantorovich value functions. The feasible set consists of vectors of probabilities increasing in the convex order, ensuring that the data generated by the solution is arbitrage-free. Depending on the application, we motivate how cost functions of Monge-Kantorovich problems can be chosen. We illustrate the method with concrete examples. To handle signed input marginals that appear when the input implied volatilities exhibit arbitrage, we introduce a generalized notion of couplings beyond the classical nonnegative case. Under suitable assumptions, our generalization recovers known results in the nonnegative setting.

Computing the implied volatility through neural networks with asymptotic regimes

Samira Amiriyan (University of Liverpool) · Youness Boutaib (University of Liverpool)

Accurate and efficient computation of implied volatility is a fundamental problem in financial mathematics, with important applications to option pricing, model calibration, and risk management. Recent studies have explored neural-networks for this task, but existing approaches often lose precision in extreme regimes, such as very small or large strikes and maturities. In this paper, we propose a neural-network architecture that incorporates key structural features of implied volatility surfaces directly into the learning process. Inspired by Jäckel's regime-based methodology, we partition the price--log-moneyness domain into three regions and train the model to learn both a suitable partition of unity and regime-specific approximations of implied volatility. Numerical results show that the proposed design improves robustness and generalisation across the whole domain, delivering more accurate and more stable predictions than standard neural-network methods and widely used asymptotic approximations. This work links machine learning for finance, volatility modelling, and derivatives pricing through structure-aware methods.

Convex Volatility Interpolation

Fabrice Deschâtres (Volptima)

Convex volatility interpolation (CVI) casts the problem of fitting arbitrage-free implied volatility surfaces as quadratic programming in variance space. It introduces a dual parametrisation in cubic spline and B-spline spaces, mapping intuitive, dimensionless parameters to the weights of basis functions. Static arbitrage constraints, butterfly and calendar spread, are enforced through linear inequalities. This paper derives and linearises the no-butterfly-arbitrage constraints within the CVI cubic spline parameter space. Notably, the no-butterfly-arbitrage condition is derived in closed form in the linear variance extrapolation region beyond the edge knots. The formulation is model-free, bid-ask-aware, and requires no hyperparameter tuning, working consistently across underlyings. Convexity guarantees a unique global optimum, eliminating the calibration fragility of parametric approaches. Using the Clarabel conic solver, CVI fits the full S&P 500 surface, 14,500 bid-ask quotes across 46 expiries, in 0.15 seconds.

Approximation of the implied volatility surface with Hermite functions

Guido Germano (University College London) · Lorenzo Lombardi (Università degli Studi di Salerno) · Carlo Marinelli (University College London)

We study an approximation of the implied volatility surface based on projecting the square root of the density function of the logarithmic return of the underlying on finite-dimensional vector spaces of L²(ℝ) generated by Hermite functions with time-dependent scale and shift parameters. The logarithmic return at time t is approximated in law by the expression α(t)X+β(t), where α(t)=a√t+bt, with a and b constants, X a random variable admitting a density, and β specified in terms of α. A semiparametric approximation scheme is then obtained expanding the density of X in terms of the square of a linear combination of Hermite functions up to order N. The Black-Scholes model is included as a particular case for N=0. We empirically test our approximations with N=0,...,8 (d=N+2 degrees of freedom) on a EUR-USD implied volatility surface and compare their accuracy to that of Heston (d=5) and double Heston (d=10) models.

Credit - Equity Revisited

Matthias Arnsdorf (JP Morgan Chase)

Most counterparties do not have traded Credit Default Swap (CDS) instruments. This poses a challenge for calculating the Counterparty Valuation Adjustment (CVA) which relies on risk-neutral default probabilities. Here we present a new model for the estimation of credit spreads using equity market data. In contrast to more traditional credit-equity models, we take an empirical approach in order to determine a simple functional relationship that can be used in practice for CVA risk management. We find that our model out-performs models that rely solely on credit data as well as alternative credit-equity models in the literature.

BSDEs anticipated in conditional distribution : existence, comparison, Feynman-Kac representation, and approximation

Stéphane Crépey (Université Paris Cité) · Aurélien Grenard (Sorbonne University) · Cyril Bénézet (ENSIIE)

In this work, we introduce and study a class of anticipated backward stochastic differential equations (ABSDEs) whose driver depends on the conditional distribution of a functional of the solution in the future. This framework unifies and extends previous works on ABSDEs, including those where the dependence occurs through conditional expectations or conditional risk measures, e.g. the FVA and KVA ABSDE system that arises when one accounts for the fungibility of capital at risk and variation margin. Under suitable assumptions, we establish a priori estimates, existence and uniqueness of square integrable solutions, and a comparison principle. In the Markovian case, we prove that the solution admits a Feynman-Kac representation in terms of a deterministic function of the underlying factor process. This value function solves a PDE nonlocal in both time and space in the viscosity sense. Last, we show that an implicit ABSDE time-discretization scheme achieves the classical square-root convergence rate.

Branching Simulation for Evaluation of Conditional Expectations

Anas Bakkali (NatWest Markets) · Andrew Greene (NatWest Markets) · Nikolai Nowaczyk (NatWest Markets) · Vladimir Piterbarg (NatWest Markets)

High-performance pricing engines are central to XVA and counterparty credit risk. Methods such as Longstaff-Schwartz regression have been widely used, but assessing their performance has always been a challenge. Traditionally, benchmarking requires either: Costly nested MC simulations, analytical pricers (often unavailable for exotics), or statistical approaches that rely on assumptions that often don't hold.

We present a branching simulation method that:

• Computes a mean squared pricing error for any given pricer without nested Monte Carlo or knowledge of the true analytical price;
• Is fast, assumption free and easy to monitor;
• Guides model choices (e.g. feature selection, polynomial degree in regression pricers);
• Derives conservative bounds for CVA error, and then tightens them using forward MtM moments from multi-branch simulations;
• Enables automated goodness-of-fit assessments for pricing models.

Schrödinger bridge problem via empirical risk minimisation

Denis Belomestny (Duisburg-Essen University) · Aleksey Naumov (HSE) · Nikita Puchkin (HSE)

We study the Schrödinger bridge problem when the endpoint distributions are available only through samples. Classical computational approaches estimate Schrödinger potentials via Sinkhorn iterations on empirical measures and then construct a time-inhomogeneous drift by differentiating a kernel-smoothed dual solution. In contrast, we propose a learning-theoretic route: we rewrite the Schrödinger system in terms of a single positive transformed potential that satisfies a nonlinear fixed-point equation and estimate this potential by empirical risk minimization over a function class. We establish uniform concentration of the empirical risk around its population counterpart under sub-Gaussian assumptions on the reference kernel and terminal density. We plug the learned potential into a stochastic control representation of the bridge to generate samples. We illustrate performance of the suggested approach with numerical experiments.

Post-training Discrete Diffusion models via RL

Wenpin Tang (Columbia University)

We formulate RL in continuous time with discrete state spaces via a stochastic control approach, where the state dynamics are a controlled continuous-time Markov chain. We consider policy optimization problems and derive the policy gradient methods, leading to continuous-time variants of PPO and group GRPO. As an application, we develop a complete continuous-time RL framework for fine-tuning discrete diffusion models. In contrast to the existing GRPO-based approaches that only rely on terminal rewards, our formulation allows intermediate reward to be incorporated throughout the denoising trajectory. When specialized to masked diffusion models (MDMs), our framework encompasses a rich class of policy parameterizations over the vocabulary simplex with analytically tractable probability ratios, providing a unified perspective on exploration and policy optimization in MDMs. For masked diffusion large language models (dLLMs), we further propose trajectory subsampling techniques to efficiently estimate computationally prohibitive trajectory likelihoods, reducing the computational cost of computing per-position probability ratios.

Schrödinger bridge with transport relaxation

Yifan Jiang (Imperial College London)

Motivated by modern machine learning applications where we only have access to empirical measures constructed from finite samples, we relax the marginal constraints of the classical Schrödinger bridge problem by penalizing the transport cost between the bridge’s marginals and the prescribed marginals. We derive a duality formula for this transport-relaxed bridge and demonstrate that it reduces to a finite-dimensional concave optimization problem when the prescribed marginals are discrete and the reference distribution is absolutely continuous. We establish the existence and uniqueness of solutions for both the primal and dual problems. Moreover, as the penalty blows up, we characterize the limiting bridge as the solution to a discrete Schrödinger bridge problem and identify a leading-order logarithmic divergence. Finally, we propose gradient ascent and Sinkhorn-type algorithms to numerically solve the transport-relaxed Schrödinger bridge, establishing a linear convergence rate for both algorithms.

Duality Theory and DeepMartingale for High-Dimensional Optimal Switching: Computable Upper Bounds and Expressivity Guarantees

Junyan Ye (The Chinese University of Hong Kong) · Hoi Ying Wong (The Chinese University of Hong Kong)

We study finite-horizon optimal switching with discrete intervention dates on a general filtration, allowing continuous-time observations between decision dates, and develop a deep-learning-based dual framework with computable upper bounds. We derive a dual representation via martingale penalties, whose minimal form is given by the Doob martingales of continuation values, yielding a fully computable upper bound. Extending DeepMartingale from optimal stopping to optimal switching, we prove convergence under both the upper-bound loss and an L²-surrogate loss. We also establish expressivity guarantees: for any ε>0, there exist neural networks of size at most cd^qε^−r, with c, q, r independent of d and ε, whose induced dual upper bound is within ε of the true value, thus avoiding the curse of dimensionality. Combined with a deep primal policy method, our solver delivers tight bounds and practical delta hedging in Brownian and Brownian-Poisson models.

Neural network approximations for stochastic control problems with degenerate dynamics

Olivier Bokanowski (LJLL, Université Paris Cité) · Jean-François Chassagneux (ENSAE-CREST, Institut Polytechnique de Paris) · Marco Scaratti (University of Verona) · Xavier Warin (EDF, France)

We consider numerical approximations of stochastic optimal control problems over a finite time horizon. We establish new explicit error bounds, together with a convergence result for the associated value function in an averaged sense. The analysis is based on neural network approximations of optimal feedback controls. Compared with existing approaches, our framework provides an improved error estimate and accommodates degenerate stochastic diffusions. Numerical simulations illustrate the relevance of the proposed approach.

Adaptive Partitioning and Learning for Stochastic Control of Diffusion Processes

Hanqing Jin (University of Oxford) · Renyuan Xu (Stanford University) · Yanzhao Yang (University of Oxford)

We study reinforcement learning for controlled diffusion processes with unbounded continuous state spaces, bounded continuous actions, and polynomially growing rewards: settings that arise naturally in finance. To overcome the challenges of continuous and high-dimensional domains, we introduce a model-based algorithm that adaptively partitions the joint state-action space. The algorithm maintains estimators of drift, volatility, and rewards within each partition, refining the discretization whenever estimation bias exceeds statistical confidence. This adaptive scheme balances exploration and approximation, enabling efficient learning in unbounded domains. Our analysis establishes regret bounds that depend on the problem horizon, state dimension, reward growth order, and a newly defined notion of zooming dimension tailored to unbounded diffusion processes. The bounds recover existing results for bounded settings as a special case, while extending theoretical guarantees to a broader class of diffusion-type problems. Finally, we validate the effectiveness of our approach through numerical experiments, including multi-asset mean-variance portfolio selection.

Semi-analytical pricing of American options and Flexible Forward contracts via integral equations and the GIT method

Andrey Itkin (New York University)

We present a semi-analytical approach for pricing American options and FF contracts including assets paying discrete or continuous dividends. Our method leverages the Generalized Integral Transform (GIT), which reframes the pricing problem - traditionally a complex partial differential equation with a free boundary - as a Volterra integral equation of the first kind. By solving this integral equation, we can efficiently determine both the option price and the early exercise boundary while naturally accommodating the discontinuities introduced by discrete dividends. This methodology offers a powerful alternative to standard numerical techniques like binomial trees or finite difference methods, which often struggle with the jump conditions from discrete dividends, leading to a loss of accuracy or performance.

Fourier-Laplace Transform Discontinuities and Computation in the Volterra Stein-Stein Model: A Fredholm--Wishart Approach

Maxime Guellil (École Polytechnique) · Eduardo Abi Jaber (École Polytechnique)

We investigate analytical and numerical challenges in computing the Fourier-Laplace transform for the Volterra Stein-Stein model, where volatility is driven by a Volterra-type Gaussian process. A central difficulty arises from the complex square root of a Fredholm determinant, which becomes discontinuous when crossing the negative real axis. We characterize these crossings and derive a corrected expression for the joint transform of log-price and integrated variance. We further propose a derivation based on an infinite-dimensional Wishart limit, yielding a convergent numerical scheme with explicit convergence rate. Our method significantly improves accuracy while drastically reducing computational cost relative to existing approaches.

Pricing European Options using the Gauss-Laguerre Quadrature

Andrea Perchiazzo (Università Del Piemonte Orientale)

In this work we propose a novel method for pricing European options numerically in an efficient manner using the Gauss-Laguerre quadrature. Instead of employing the Carr-Madan formula, which needs an appropriate choice for the damping factor, or the COS method in which three approximation errors are introduced (e.g., truncation of the integration range in the risk-neutral valuation formula), the pricing of European options using the characteristic function is based on the Gauss-Laguerre quadrature. The approach does not necessitate the truncation of the integration range in the risk-neutral valuation formula and the approximation error term is controlled by the order of Laguerre polynomials. The new methodology is initially tested on the Black-Scholes model in order to confirm its efficacy and then applied to several models (e.g., the Merton, Kou, Variance Gamma, and Heston models). Finally, we provide a benchmarking exercise between the Gauss-Laguerre-based approach, the COS method, and the Carr--Madan formula.

Short-rate models with stochastic discontinuities: a PDE approach.

Alessandro Calvia (Politecnico di Milano) · Marzia De Donno (Università Cattolica del Sacro Cuore) · Chiara Guardasoni (Università di Parma) · Simona Sanfelici (Università di Parma)

In the ongoing reform of interest rate benchmarks, risk-free rates (RFRs), such as the Secured Overnight Financing Rate (SOFR) in the U.S. or the Euro Short-Term Rate (€STR) in Europe, play a pivotal role. An observed characteristic of RFRs is the occurrence of jumps and spikes at regular intervals, due to regulatory and liquidity constraints. In this paper, we consider a general short-rate model featuring discontinuities at fixed times with random sizes. Within this framework, we introduce a PDE-based approach to price interest rate derivatives. For affine models, we also derive (quasi) closed-form solutions. Finally, we develop numerical methods to price interest rate derivatives in general cases.

Stochastic factors can matter: improving robust growth under ergodicity

Paul Mangers Bastian (The London School of Economics and Political Science) · Josef Teichmann (ETH Zurich) · David Itkin (The London School of Economics and Political Science) · Balint Binkert (ETH Zurich)

We study robust growth optimization in a high-dimensional incomplete market under drift uncertainty of the asset price process X, under an additional ergodicity assumption, which constrains but does not fully specify the drift in general. The class of admissible models allows X to depend on a multivariate stochastic factor Y and fixes (a) their joint volatility structure, (b) their long-term joint ergodic density and (c) the dynamics of the stochastic factor process Y. Our main results determine the robust optimal growth rate, construct a worst-case admissible model and characterize the robust growth-optimal strategy via a solution to a certain partial differential equation (PDE). Our analysis leads to new financial insights, quantifying the improvement in growth the investor can achieve by optimally incorporating stochastic factors into their trading decisions. We illustrate our theoretical results on several numerical examples including an application to pairs trading.

Cancelled: Scalable Bi-causal Optimal Transport via Kullback--Leibler Relaxation and Policy Gradients

Haoyang Cao (Johns Hopkins University) · Jesse Hoekstra (University of Oxford) · Renyuan Xu (Stanford University) · Yumin Xu (Peking University) · Ruixun Zhang (Peking University)

Bi-causal optimal transport (OT) is a natural framework for comparing and coupling stochastic processes under nonanticipative information constraints, with important applications in computational finance. Its practical use, however, is limited by the computational difficulty of enforcing bi-causal coupling constraints over path space. We develop a scalable stochastic-optimization framework for computing bi-causal OT couplings under general marginals. Our approach introduces a Kullback--Leibler-penalized relaxation that replaces hard marginal constraints with tractable divergence penalties. We establish dynamic programming principles for both the original and relaxed formulations, prove that the relaxed problem converges to the original bi-causal OT problem as the penalty grows, and derive explicit policy-gradient representations for the relaxed objective. Building on these results, we propose a practical policy-gradient algorithm with nonasymptotic regret guarantees. Numerical experiments show that the method accurately captures marginal laws and temporal dependence, and performs well in applications including robust subhedging and time-series statistical downscaling.

Numerical approximation of forward-backward SDEs with jumps and application to emission markets

Joao Guerra (Lisbon School of Economics and Management) · Gonçalo Fonseca (Lisbon School of Economics and Management)

In this work, we study a numerical approximation method for coupled forward-backward stochastic differential equations with jumps of finite activity measure. We assume that the coefficients are Lipschitz continuous and satisfy some appropriate weak coupling or monotonicity conditions and we propose a method that combines a Picard/Markov iteration procedure with a time discretization consistent with jumps. We suggest a explicit numerical algorithm and we explore an application to a carbon emissions market.

Optimal Consumption and Investment with Energy-Efficiency Adoption

Anthony Britto (Karlsruhe Institute of Technology) · Carlos Miguel Dos Santos Oliveira (Lisbon School of Economics and Management) · Max Kleinebrahm (Karlsruhe Institute of Technology)

This article develops a unified model of consumption, investment, and energy-efficiency adoption under uncertainty. It introduces new definitions of rebound and backfire effects and incorporates their welfare implications into optimal subsidy design. The model formalises macro-level technology diffusion and energy consumption across heterogeneous agents. Explicit expressions are derived for key objects, including the adoption threshold and post-adoption strategies, which depend on agent wealth and reveal a new channel through which financial conditions influence adoption decisions. A case study of a representative German single-family home illustrates the results, and numerical simulations show that the designed subsidy policy effectively guides aggregate energy consumption

Approximate computation of the probability of Parisian ruin and optimal reinsurance

Manuel Guerra (Lisbon School of Economics and Management) · Phuong Nguyen (Lisbon School of Economics and Management; CEMAPRE)

Parisian ruin allows for a grace period after the company's reserve goes below a critical threshold. If the company manages to sort its finances during this period, it avoids ruin and may continue its business. Otherwise, so called "Parisian ruin" occurs.

General closed form expressions for the probability of Parisian ruin given the initial level of reserves are not available. In this study, we present an approximate formula and apply it to the computation of optimal reinsurance treaties from the cedent's point of view.

Market-implied time to transition to a low-carbon economy from the greenium term structure

Lorenzo Mercuri (Università Degli Studi Di Milano) · Andrea Perchiazzo (Università Del Piemonte Orientale) · Edit Rroji (Univesità Degli Studi di Milano-Bicocca) · Ilaria Stefano (Univesità Degli Studi di Milano-Bicocca)

We analyze the term structure of the greenium by means of a novel class of constrained stochastic processes. We introduce the Stochastic Regulatory Deadline-Constrained Model (SRDCM), a regime-switching framework in which greenium differentials are described by a sequence of stochastic bridges targeting terminal alignment at a policy deadline T. To handle the singular behavior of bridge processes near the deadline, we develop an inference procedure based on a path-specific gap condition. Under this condition, we derive a tractable high-frequency limit for the switching contrast function and show that the diffusion block is identified at first order. The model provides a flexible framework for extracting market-implied transition timing under deadline uncertainty and regime shifts.

https://papers.ssrn.com/sol3/papers.cfm?abstract_id=6135666

Cancelled: Rough differential equations for volatility

Ofelia Bonesini (The London School of Economics)

We introduce a canonical way of performing the joint lift of a Brownian motion W and a low-regularity adapted stochastic rough path X. Applying this construction to the case where X is the canonical lift of a one-dimensional fractional Brownian motion (possibly correlated with W) completes the partial rough path of Fukasawa and Takano. We use this to model rough volatility with the versatile toolkit of rough differential equations (RDEs), namely by taking the price and volatility processes to be the solution to a single RDE. The lead-lag scheme of Flint, Hambly, and Lyons is extended to our fractional setting as an approximation theory for the rough path in the correlated case. Continuity of the solution map transforms this into a numerical scheme for RDEs. We numerically test this framework and use it to calibrate a simple new rough volatility model to market data.

A Unified Theory of Order Flow, Market Impact and Volatility

Mathieu Rosenbaum (Université Paris-Dauphine)